Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
848 conjugacy classes of subgroups; only the 157 normal subgroups are shown.
This group has 848 conjugacy classes of subgroups — too many to draw. Only its 157 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×#15690731 | C2 | semidirect |
| 2. C2×C22⋊#11715895 | C2 | semidirect |
| 3. #20260595 | C2 | semidirect |
| 5. C22×#11715895 | C22 | semidirect |
| 6. C2×C4⋊Dic97 | C22 | semidirect |
| 15. C22×D4×C97 | C4 | semidirect |
| 62. D4×C97 | C22⋊C4 | semidirect |
| 84. C22×C97 | #102 | semidirect |
| 102. C97 | #1786 | semidirect |
| 111. C22×D4 | Dic97 | semidirect |
| 164. D4 | C22⋊Dic97 | semidirect |
| 186. C22 | #15690731 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#15690731 | 2 |
| C2×C22⋊#11715895 | 2 |
| #20260595 | 2 |
| C23×D4×C97 | 2 |
| #1786 | 97 |